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A202604 Clique number for the n-Keller graph. 4
1, 2, 5, 12, 28, 60, 124, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824, 2147483648, 4294967296, 8589934592 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) <= 2^n.

a(7) = 124 was established by Debroni et al. (2011).

a(8) = 2^8 was established by Mackey (2002).

a(n) = 2^n for n >= 8 (see Jarnicki et al.).

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

J. Debroni, J. D. Eblen, M. A. Langston, P. Shor, W. Myrvold, D. Weerapurage, A complete resolution of the Keller maximum clique problem, Proceedings of the 22nd ACM-SIAM Symposium on Discrete Algorithms, pp. 129-135, 2011.

Witold Jarnicki, W. Myrvold, P. Saltzman, S. Wagon, Properties, Proved and Conjectured, of Keller, Mycielski, and Queen Graphs, arXiv preprint arXiv:1606.07918 [math.CO], 2016.

J. Mackey, A cube tiling of dimension eight with no facesharing, Discrete & Computational Geometry 28 (2): 275-279, 2002.

Eric Weisstein's World of Mathematics, Clique Number

Eric Weisstein's World of Mathematics, Keller Graph

Index entries for linear recurrences with constant coefficients, signature (2).

FORMULA

G.f.: x*(1 + x^2 + 2*x^3 + 4*x^4 + 4*x^5 + 4*x^6 + 8*x^7) / (1 - 2*x). - Colin Barker, Oct 14 2017

MATHEMATICA

Table[Piecewise[{{1, n == 1}, {2, n == 2}, {5, n == 3}, {2^n - 4, 4 <= n <= 7}}, 2^n], {n, 20}] (* Eric W. Weisstein, Mar 21 2018 *)

Join[{1, 2, 5, 12, 28, 60, 124}, LinearRecurrence[{2}, {256}, 14]] (* Eric W. Weisstein, Mar 21 2018 *)

CoefficientList[Series[(-1 - x^2 - 2 x^3 - 4 x^4 - 4 x^5 - 4 x^6 - 8 x^7)/(-1 + 2 x), {x, 0, 20}], x] (* Eric W. Weisstein, Mar 21 2018 *)

PROG

(PARI) Vec(x*(1 + x^2 + 2*x^3 + 4*x^4 + 4*x^5 + 4*x^6 + 8*x^7) / (1 - 2*x) + O(x^40)) \\ Colin Barker, Oct 14 2017

CROSSREFS

Cf. A295902, A296100, A296101.

Sequence in context: A316706 A171579 A228638 * A118898 A111586 A192657

Adjacent sequences:  A202601 A202602 A202603 * A202605 A202606 A202607

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, Dec 21 2011

EXTENSIONS

More terms from N. J. A. Sloane, Jul 04 2017 based on the Jarnicki et al. survey.

STATUS

approved

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Last modified December 7 09:33 EST 2019. Contains 329843 sequences. (Running on oeis4.)